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arXiv:2601.14513 · Annalen der Physik

Spin-$s$ $U(1)$-eigenstate preparation

Nabi Zare Harofteh, Rafael I. Nepomechie

quant-phSubmitted Jan 20, 2026• Announced Jan 22, 2026• 0 citations
v1 · Jan 20, 2026v2 · Jun 27, 2026v3 · Aug 4, 2026
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Abstract

We formulate a deterministic algorithm for preparing a general $U(1)$-eigenstate of a spin-$s$ chain of length $n$. These states consist of linear combinations of computational basis states $|\vec{m}\rangle$ of $n$ qudits, each with $(2s+1)$ levels and $s= 1/2, 1, 3/2, \ldots$, whose ditstrings $\vec{m}$ have a fixed digit sum. Exploiting a Gray code for bounded integer compositions, whose consecutive ditstrings obey the Gray property, the quantum state is prepared by applying corresponding ``Gray gates.'' We use this algorithm to prepare exact eigenstates of integrable spin-$s$ XXX Hamiltonians.

Journal reference
Annalen der Physik, 2026; 538:e70239
DOI
10.1002/andp.70239
Comments
13 pages, 3 figures, implementations of circuits in cirq are available on GitHub

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